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A5-2 Synch Lesson

Last updated over 4 years ago
20 questions
For today's lesson, we are going to:
- Practice multiplying binomials
- Focus on the patterns
- Reverse the process
For the next few problems, you'll be multiplying binomials.

When we multiply these binomials, we get


To enter the answer, you will enter only the middle and last term (for now, the x-squared won't change). So, for this answer, you would type in 5x, 6
1

Multiply and simplify

To type in your answer, fill in the blanks, separated by a comma, then a space.

1

Multiply and simplify

To type in your answer, fill in the blanks, separated by a comma, then a space.

1

Multiply and simplify

To type in your answer, fill in the blanks, separated by a comma, then a space.

If you struggled with the first three problems, watch the video below to see two different methods of multiplying binomials. If you feel comfortable, you can skip it.
Today, we'll be focusing on the patterns that we see when we multiply binomials. We'll then use the pattern to reverse the process, which is called factoring. First, we need some common vocabulary. When you multiply binomials (also called binomial factors), we typically end up with a quadratic expression or equation (at least we do for this unit). This is the most common form:

Where "a" is the coefficient (number multiplied by) the x-squared (or x to the second power), "b" is the coefficient for x, and c is a constant (a number with no variable attached).
Look at the four problems below. What pattern do you notice about the parts highlighted in green? (you don't need to enter an answer, just think about it.


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Let's generalize (create a formula) for multiplying two binomials
When multiplied out, the "b" value for this quadratic expression is:

Look at the four problems below. What pattern do you notice about the parts highlighted in yellow?


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Let's generalize (create a formula) for multiplying two binomials
When multiplied out, the "c" value for this quadratic expression is:

If that made sense to you, great! If not, watch the video below.
Now, we need to reverse the process by factoring a quadratic. In other words, we want to take a quadratic expression and figure out what binomials multiply to give you that quadratic.
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Let's start by factoring a number, and keeping those factors in pairs. Which of the following are factors of 30? (which pairs will multiply to equal 30)

Finding all the whole number factors of a number is much easier if you have the muliplication table memorized, but there is also a simple way to do it if you struggle to remember your multiplication table. This method is also helpful when you are trying to figure out what numbers go into the binomial factors.
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Which pairs of binomial factors might multiply to give us the quadratic below? (we can't know for sure if we don't know "b")

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Which pairs of binomial factors might multiply to give us the quadratic below? (we can't know for sure if we don't know "b")

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Which pairs of binomial factors might multiply to give us the quadratic below? (we can't know for sure if we don't know "b")

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Now that we know the "b" value, what is the factored form of the quadratic (meaning, which pair of binomials multiply to give us the quadratic below?

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Now that we know the "b" value, what is the factored form of the quadratic (meaning, which pair of binomials multiply to give us the quadratic below?

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Now that we know the "b" value, what is the factored form of the quadratic (meaning, which pair of binomials multiply to give us the quadratic below?

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How did you know which pair of binomial factors to choose once you knew the middle term ("b" value)?

If you struggled with any of the last 6 problems, the video below may help.
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Find the factored form of the quadratic below. For many, you may need some scratch paper.

To type your answer, be sure that both binomial factors have parentheses around them and that you haven't put any spaces.

1

Find the factored form of the quadratic below. For many, you may need some scratch paper.

To type your answer, be sure that both binomial factors have parentheses around them and that you haven't put any spaces.

1

Find the factored form of the quadratic below. For many, you may need some scratch paper.

To type your answer, be sure that both binomial factors have parentheses around them and that you haven't put any spaces.

1

Find the factored form of the quadratic below. For many, you may need some scratch paper.

To type your answer, be sure that both binomial factors have parentheses around them and that you haven't put any spaces.

Looking ahead
Next class, we're going to be working with factoring binomials when the quadratic includes negative numbers. Try the problems below to see why we might need to be more careful with those!
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When multiplied out, the two problems below result in the same quadratic expression.


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What part or parts of the equation will be different, if any?


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How do you feel about factoring a quadratic expression like the problems in this activity (not including the last two)? What do you need help with? What do you need more practice with?